In a large bowl, cream together butter and sugar until smooth.
Beat in egg and vanilla.

Stir in the flour, baking powder, and salt.
Cover, and chill dough for at least one hour (or overnight).
Preheat oven to 400 degrees F.
Roll out dough on floured surface 1/4 to 1/2 inch thick.
Cut into shapes with any cookie cutter.

Place cookies 1 inch apart on ungreased cookie sheets.
Bake 6 to 8 minutes in preheated oven.

Cool completely.